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Manu: minor changes in II A

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Emmanuel Fromager 2020-02-28 16:24:33 +01:00
parent 33060b9163
commit 0ffa8557f4
1 changed files with 5 additions and 2 deletions
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Manuscript/eDFT.tex
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@ -254,7 +254,10 @@ Atomic units are used throughout.
\subsection{GOK-DFT}\label{subsec:gokdft}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The GOK ensemble energy~\cite{Gross_1988a,Oliveira_1988,Gross_1988b} is defined as
In this section we give a brief review of GOK-DFT and discuss the
extraction of individual energy levels \cite{Deur_2019,Fromager_2020} with a particular focus on exact
individual exchange energies.
Let us start by introducing the GOK ensemble energy~\cite{Gross_1988a}:
\beq\label{eq:exact_GOK_ens_ener}
\E{}{\bw}=\sum_{K \geq 0} \ew{K} \E{}{(K)},
\eeq
@ -271,7 +274,7 @@ They are normalized, \ie,
so that only the weights $\bw \equiv \qty( \ew{1}, \ew{2}, \ldots, \ew{K}, \ldots )$ assigned to the excited states can vary independently.
For simplicity we will assume in the following that the energies are not degenerate.
Note that the theory can be extended to multiplets simply by assigning the same ensemble weight to all degenerate states~\cite{Gross_1988b}.
In the KS formulation of GOK-DFT, \manu{which is simply referred to as
In the KS formulation of GOK-DFT, {which is simply referred to as
KS ensemble DFT (KS-eDFT) in the following}, the ensemble energy is determined variationally as follows~\cite{Gross_1988b}:
\beq\label{eq:var_ener_gokdft}
\E{}{\bw}